Turbulent mixing in a shear-free stably stratified two-layer fluid

1998 ◽  
Vol 354 ◽  
pp. 175-208 ◽  
Author(s):  
DAVID A. BRIGGS ◽  
JOEL H. FERZIGER ◽  
JEFFREY R. KOSEFF ◽  
STEPHEN G. MONISMITH
Keyword(s):  
Kinetic Energy ◽  
Froude Number ◽  
Internal Waves ◽  
Mixed Layer ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Source Region ◽  
Buoyancy Flux ◽  
Mixing Efficiency ◽  
Principal Mechanism

Direct numerical simulation is used to examine turbulent mixing in a shear-free stably stratified fluid. Energy is continuously supplied to a small region to maintain a well-developed kinetic energy profile, as in an oscillating grid flow (Briggs et al. 1996; Hopfinger & Toly 1976; Nokes 1988). A microscale Reynolds number of 60 is maintained in the source region. The turbulence forms a well-mixed layer which diffuses from the source into the quiescent fluid below. Turbulence transport at the interface causes the mixed layer to grow under weakly stratified conditions. When the stratification is strong, large-scale turbulent transport is inactive and pressure transport becomes the principal mechanism for the growth of the turbulence layer. Down-gradient buoyancy flux is present in the large scales; however, far from the source, weak counter-gradient fluxes appear in the medium to small scales. The production of internal waves and counter-gradient fluxes rapidly reduces the mixing when the turbulent Froude number is lower than unity. When the stratification is weak, the turbulence is strong enough to break up the density interface and transport fluid parcels of different density over large vertical distances. As the stratification intensifies, turbulent eddies flatten against the interface creating anisotropy and internal waves. The dominant entrainment mechanism is then scouring. Mixing efficiency, defined as the ratio of buoyancy flux to available kinetic energy, exhibits a similar dependence on Froude number to other stratified flows (Holt et al. 1992; Lienhard & Van Atta 1990). However, using the anisotropy of the turbulence to define an alternative mixing efficiency and Froude number improves the correlation and allows local scaling.

Local versus volume-integrated turbulence and mixing in breaking internal waves on slopes

2017 ◽  
Vol 815 ◽  
pp. 169-198 ◽  
Author(s):  
Robert S. Arthur ◽  
Jeffrey R. Koseff ◽  
Oliver B. Fringer
Keyword(s):  
Froude Number ◽  
Internal Waves ◽  
Turbulent Mixing ◽  
Wave Breaking ◽  
Mixing Efficiency ◽  
Breaking Wave ◽  
Incoming Wave ◽  
Turbulent Dissipation ◽  
Efficiency Measures ◽  
Wave Properties

Using direct numerical simulations (DNS), we explore local and volume-integrated measures of turbulence and mixing in breaking internal waves on slopes. We consider eight breaking wave cases with a range of normalized pycnocline thicknesses $k\unicode[STIX]{x1D6FF}$, where $k$ is the horizontal wavenumber and $\unicode[STIX]{x1D6FF}$ is the pycnocline thickness, but with similar incoming wave properties. The energetics of wave breaking is quantified in terms of local turbulent dissipation and irreversible mixing using the method of Scotti & White (J. Fluid Mech., vol. 740, 2014, pp. 114–135). Local turbulent mixing efficiencies are calculated using the irreversible flux Richardson number $R_{f}^{\ast }$ and are found to be a function of the turbulent Froude number $Fr_{k}$. Volume-integrated measures of the turbulent mixing efficiency during wave breaking are also made, and are found to be functions of $k\unicode[STIX]{x1D6FF}$. The bulk turbulent mixing efficiency ranges from 0.25 to 0.37 and is maximized when $k\unicode[STIX]{x1D6FF}\approx 1$. In order to connect local and bulk mixing efficiency measures, the variation in the bulk turbulent mixing efficiency with $k\unicode[STIX]{x1D6FF}$ is related to the turbulent Froude number at which the maximum total mixing occurs over the course of the breaking event, $Fr_{k}^{max}$. We find that physically, $Fr_{k}^{max}$ is controlled by the vertical length scale of billows at the interface during wave breaking.

Entrainment and mixing in stratified shear flows

2001 ◽  
Vol 428 ◽  
pp. 349-386 ◽  
Author(s):  
E. J. STRANG ◽  
H. J. S. FERNANDO
Keyword(s):  
Internal Waves ◽  
Richardson Number ◽  
Transition Period ◽  
Lower Layer ◽  
Buoyancy Flux ◽  
Shear Instability ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Entrainment Rate ◽  
Turbulent Eddies

The results of a laboratory experiment designed to study turbulent entrainment at sheared density interfaces are described. A stratified shear layer, across which a velocity difference ΔU and buoyancy difference Δb is imposed, separates a lighter upper turbulent layer of depth D from a quiescent, deep lower layer which is either homogeneous (two-layer case) or linearly stratified with a buoyancy frequency N (linearly stratified case). In the parameter ranges investigated the flow is mainly determined by two parameters: the bulk Richardson number RiB = ΔbD/ΔU2 and the frequency ratio fN = ND=ΔU.When RiB > 1.5, there is a growing significance of buoyancy effects upon the entrainment process; it is observed that interfacial instabilities locally mix heavy and light fluid layers, and thus facilitate the less energetic mixed-layer turbulent eddies in scouring the interface and lifting partially mixed fluid. The nature of the instability is dependent on RiB, or a related parameter, the local gradient Richardson number Rig = N2L/ (∂u/∂z)2, where NL is the local buoyancy frequency, u is the local streamwise velocity and z is the vertical coordinate. The transition from the Kelvin–Helmholtz (K-H) instability dominated regime to a second shear instability, namely growing Hölmböe waves, occurs through a transitional regime 3.2 < RiB < 5.8. The K-H activity completely subsided beyond RiB ∼ 5 or Rig ∼ 1. The transition period 3.2 < RiB < 5 was characterized by the presence of both K-H billows and wave-like features, interacting with each other while breaking and causing intense mixing. The flux Richardson number Rif or the mixing efficiency peaked during this transition period, with a maximum of Rif ∼ 0.4 at RiB ∼ 5 or Rig ∼ 1. The interface at 5 < RiB < 5.8 was dominated by ‘asymmetric’ interfacial waves, which gradually transitioned to (symmetric) Hölmböe waves at RiB > 5:8.Laser-induced fluorescence measurements of both the interfacial buoyancy flux and the entrainment rate showed a large disparity (as large as 50%) between the two-layer and the linearly stratified cases in the range 1.5 < RiB < 5. In particular, the buoyancy flux (and the entrainment rate) was higher when internal waves were not permitted to propagate into the deep layer, in which case more energy was available for interfacial mixing. When the lower layer was linearly stratified, the internal waves appeared to be excited by an ‘interfacial swelling’ phenomenon, characterized by the recurrence of groups or packets of K-H billows, their degeneration into turbulence and subsequent mixing, interfacial thickening and scouring of the thickened interface by turbulent eddies.Estimation of the turbulent kinetic energy (TKE) budget in the interfacial zone for the two-layer case based on the parameter α, where α = (−B + ε)/P, indicated an approximate balance (α ∼ 1) between the shear production P, buoyancy flux B and the dissipation rate ε, except in the range RiB < 5 where K-H driven mixing was active.

Flow Geometry Effects on the Turbulent Mixing Efficiency

2006 ◽  
Vol 128 (4) ◽  
pp. 874-879 ◽  
Author(s):  
Roberto C. Aguirre ◽  
Jennifer C. Nathman ◽  
Haris C. Catrakis
Keyword(s):  
Shear Layer ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Mixture Fraction ◽  
Mixing Efficiency ◽  
Developed Turbulence ◽  
Planar Shear ◽  
Flow Geometry ◽  
Schmidt Numbers ◽  
Geometry Effects

Flow geometry effects are examined on the turbulent mixing efficiency quantified as the mixture fraction. Two different flow geometries are compared at similar Reynolds numbers, Schmidt numbers, and growth rates, with fully developed turbulence conditions. The two geometries are the round jet and the single-stream planar shear layer. At the flow conditions examined, the jet exhibits an ensemble-averaged mixing efficiency which is approximately double the value for the shear layer. This substantial difference is explained fluid mechanically in terms of the distinct large-scale entrainment and mixing-initiation environments and is therefore directly due to flow geometry effects.

Onset of stratification in a mixed layer subjected to a stabilizing buoyancy flux

1995 ◽  
Vol 304 ◽  
pp. 27-46 ◽  
Author(s):  
Y. Noh ◽  
H. J. S. Fernando
Keyword(s):  
Numerical Model ◽  
Kinetic Energy ◽  
Laboratory Experiment ◽  
Water Column ◽  
Turbulent Kinetic Energy ◽  
Energy Flux ◽  
Mixed Layer ◽  
Mixed State ◽  
Buoyancy Flux ◽  
Tidal Front

The formation of a thermocline in a water column, in which shear-free turbulence is generated both at the surface and bottom, and a stabilizing buoyancy flux is imposed at the surface, is studied using a laboratory experiment and a numerical model with the aim of understanding the formation of a tidal front in coastal seas. The results show that the formation of a thermocline, which always occurs in the absence of bottom mixing, is inhibited and the water column maintains a vertically mixed state, when bottom mixing becomes sufficiently strong. It is found from both experimental and numerical results that the criterion for the formation of a thermocline is determined by the balance between the rate of work that is necessary to maintain a mixed state against the formation of stratification by the buoyancy flux and the turbulent kinetic energy flux from the bottom supplied to the depth of thermocline formation. The depth of the thermocline, when it is formed, is found to decrease with bottom mixing.

scholarly journals Turbulent mixing at a stable density interface: the variation of the buoyancy flux–gradient relation

2007 ◽  
Vol 577 ◽  
pp. 127-136 ◽  
Author(s):  
E. GUYEZ ◽  
J.-B. FLOR ◽  
E. J. HOPFINGER
Keyword(s):  
Turbulent Mixing ◽  
Turnover Time ◽  
Buoyancy Flux ◽  
Mixing Efficiency ◽  
Experimental Conditions ◽  
Scale Separation ◽  
Large Variability ◽  
Density Interface ◽  
First Time ◽  
Gap Width

Experiments conducted on mixing across a stable density interface in a turbulent Taylor–Couette flow show, for the first time, experimental evidence of an increase in mixing efficiency at large Richardson numbers. With increasing buoyancy gradient the buoyancy flux first passes a maximum, then decreases and at large values of the buoyancy gradient the flux increases again. Thus, the curve of buoyancy flux versus buoyancy gradient tends to be N-shaped (rather than simply bell shaped), a behaviour suggested by the model of Balmforth et al. (J. Fluid Mech. vol. 428, 1998, p. 349). The increase in mixing efficiency at large Richardson numbers is attributed to a scale separation of the eddies active in mixing at the interface; when the buoyancy gradient is large mean kinetic energy is injected at scales much smaller than the eddy size fixed by the gap width, thus decreasing the eddy turnover time. Observations show that there is no noticeable change in interface thickness when the mixing efficiency increases; it is the mixing mechanism that changes. The curves of buoyancy flux versus buoyancy gradient also show a large variability for identical experimental conditions. These variations occur at time scales one to two orders of magnitude larger than the eddy turnover time scale.

scholarly journals Near-Inertial Internal Waves and Sea Ice in the Beaufort Sea*

2014 ◽  
Vol 44 (8) ◽  
pp. 2212-2234 ◽  
Author(s):  
Kim I. Martini ◽  
Harper L. Simmons ◽  
Chase A. Stoudt ◽  
Jennifer K. Hutchings
Keyword(s):  
Kinetic Energy ◽  
Internal Wave ◽  
Internal Waves ◽  
Mixed Layer ◽  
The Arctic ◽  
Spectral Energy ◽  
Late Winter ◽  
Wave Band ◽  
Atmospheric Energy ◽  
Ice Pack

Abstract The evolution of the near-inertial internal wavefield from ice-free summertime conditions to ice-covered wintertime conditions is examined using data from a yearlong deployment of six moorings on the Beaufort continental slope from August 2008 to August 2009. When ice is absent, from July to October, energy is efficiently transferred from the atmosphere to the ocean, generating near-inertial internal waves. When ice is present, from November to June, storms also cause near-inertial oscillations in the ice and mixed layer, but kinetic energy is weaker and oscillations are quickly damped. Damping is dependent on ice pack strength and morphology. Decay scales are longer in early winter (November–January) when the new ice pack is weaker and more mobile, decreasing in late winter (February–June) when the ice pack is stronger and more rigid. Efficiency is also reduced, as comparisons of atmospheric energy available for internal wave generation to mixed layer kinetic energies indicate that a smaller percentage of atmospheric energy is transferred to near-inertial motions when ice concentrations are &gt;90%. However, large kinetic energies and shears are observed during an event on 16 December and spectral energy is elevated above Garrett–Munk levels, coinciding with the largest energy flux predicted during the deployment. A significant amount of near-inertial energy is episodically transferred to the internal wave band from the atmosphere even when the ocean is ice covered; however, damping by ice and less efficient energy transfer still leads to low Arctic internal wave energy in the near-inertial band. Increased kinetic energy below 300 m when ice is forming suggests some events may generate internal waves that radiate into the Arctic Ocean interior.

Numerical Mixing Analysis of a Vaned Circular Micromixer

2006 ◽  
Author(s):  
Richard Bergman ◽  
Alexander Efremov ◽  
Pierre Woehl
Keyword(s):  
Numerical Analysis ◽  
Turbulent Mixing ◽  
Parametric Study ◽  
Large Scale ◽  
Acceptable Level ◽  
Mixing Efficiency ◽  
Mixing Process ◽  
Mixing Performance ◽  
Numerical Mixing ◽  
Cutting And Stacking

Mixing of fluids is a common and often critical step in microfluidic systems. In typical large scale processes turbulence greatly speeds the mixing process. At the mini and micro-scales, however, the flow is laminar and the benefits of turbulent mixing are not present. Mixing at the mini- and micro-scales tends to become a more highly engineered process of bringing fluids together in predictable ways to achieve a predetermined and acceptable level of mixing. This paper summarizes a numerical analysis of the mixing performance of a vaned circular micromixer. A newly developed mixing metric suitable for reacting fluids is developed for this study. Applying the basic steps of stretching, cutting, and stacking to effect mixing, a useful micromixer is analyzed numerically for its mixing efficiency. A parametric study of flow and viscosity indicate that a flow Re of 12 or higher is sufficient to achieve effective and rapid mixing in this device.

scholarly journals Baroclinic Frontal Instabilities and Turbulent Mixing in the Surface Boundary Layer. Part I: Unforced Simulations

2012 ◽  
Vol 42 (10) ◽  
pp. 1701-1716 ◽  
Author(s):  
Eric D. Skyllingstad ◽  
R. M. Samelson
Keyword(s):  
Mixed Layer ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Wave Activity ◽  
Small Scale ◽  
Turbulent Heat ◽  
Surface Boundary ◽  
Baroclinic Wave ◽  
Baroclinic Waves ◽  
Scale Turbulence

Abstract Interaction between mixed layer baroclinic eddies and small-scale turbulence is studied using a nonhydrostatic large-eddy simulation (LES) model. Free, unforced flow evolution is considered, for a standard initialization consisting of an 80-m-deep mixed layer with a superposed warm filament and two frontal interfaces in geostrophic balance, on a model domain roughly 5 km × 10 km × 120 m, with an isotropic 3-m computational grid. Results from these unforced experiments suggest that shear generated in narrow frontal zones can support weak three-dimensional turbulence that is directly linked to the larger-scale baroclinic waves. Two separate but closely related issues are addressed: 1) the possible development of enhanced turbulent mixing associated with the baroclinic wave activity and 2) the existence of a downscale transfer of energy from the baroclinic wave scale to the turbulent dissipation scale. The simulations show enhanced turbulence associated with the baroclinic waves and enhanced turbulent heat flux across the isotherms of the imposed frontal boundary, relative to background levels. This turbulence develops on isolated small-scale frontal features that form as the result of frontogenetic processes operating on the baroclinic wave scale and not as the result of a continuous, inertial forward cascade through the intermediate scales. Analysis of the spectrally decomposed kinetic energy budget indicates that large-scale baroclinic eddy energy is directly transferred to small-scale turbulence, with weaker forcing at intermediate scales. For fronts with significant baroclinic wave activity, cross-frontal eddy fluxes computed from correlations of fluctuations from means along the large-scale frontal axis generally agreed with simple theoretical estimates.

scholarly journals Cold-Water Events and Dissipation in the Mixed Layer of a Lake

2006 ◽  
Vol 36 (10) ◽  
pp. 1928-1939 ◽  
Author(s):  
B. Ozen ◽  
S. A. Thorpe ◽  
U. Lemmin ◽  
T. R. Osborn
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Mixed Layer ◽  
Large Scale ◽  
Cold Water ◽  
Velocity Shear ◽  
Surface Mixed Layer ◽  
Near Surface ◽  
Law Of The Wall ◽  
Upward Direction

Abstract Measurements of temperature, velocity, and microscale velocity shear were made from the research submarine F. A. Forel in the near-surface mixed layer of Lake Geneva under conditions of moderate winds of 6–8 m s−1 and of net heating at the water surface. The submarine carried arrays of thermistors and a turbulence package, including airfoil shear probes. The rate of dissipation of turbulent kinetic energy per unit mass, estimated from the variance of the shear, is found to be lognormally distributed and to vary with depth roughly in accordance with the law of the wall at the measurement depths, 15–20 times the significant wave height. Measurements revealed large-scale structures, coherent over the 2.38-m vertical extent sampled by a vertical array of thermistors, consisting of filaments tilted in the wind direction. They are typically about 1.5 m wide, decreasing in width in the upward direction, and are horizontally separated by about 25 m in the downwind direction. Originating in the upper thermocline, they are characterized in the mixed layer by their relatively low temperature and low rates of dissipation of turbulent kinetic energy and by an upward vertical velocity of a few centimeters per second.

Sign in / Sign up

Export Citation Format

Share Document